Acoustic Programming in Step-Split-Flow Lateral-Transport Thin

25 Jan 2010 - Calculations in order to compare separations obtained by the acoustic programming s-SPLITT fractionation and the conventional SPLITT ...
0 downloads 0 Views 2MB Size
Download PDF
Anal. Chem. 2010, 82, 1318–1325

Acoustic Programming in Step-Split-Flow Lateral-Transport Thin Fractionation Claire Ratier and Mauricio Hoyos* Laboratoire de Physique et Me´canique des Milieux He´te´rogenes, UMR7636 CNRS, ESPCI, 10, Rue Vauquelin, 75231 Paris Cedex 05, France We propose a new separation scheme for micrometersized particles combining acoustic forces and gravitational field in split-flow lateral-transport thin (SPLITT)-like fractionation channels. Acoustic forces are generated by ultrasonic standing waves set up in the channel thickness. We report on the separation of latex particles of two different sizes in a preliminary experiment using this proposed hydrodynamic acoustic sorter, HAS. Total binary separation of 5 and 10 µm diameter particles has been achieved. Numerical simulations of trajectories of particles flowing through a step-SPLITT under the conditions which combine acoustic standing waves and gravity show a very good agreement with the experiment. Calculations in order to compare separations obtained by the acoustic programming s-SPLITT fractionation and the conventional SPLITT fractionation show that the improvement in separation time is around 1 order of magnitude and could still be improved; this is the major finding of this work. This separation technique can be extended to biomimetic particles and blood cells. Ultrasonic resonators in microfluidic devices have recently gained great interest because of the promising biomedical and biotechnological applications to water purification,1 blood fractionation,2,3 and bacteria4 and bubble focusing.5 It is well-known that particulate materials in suspension inside a cavity are sensitive to an acoustic force generated by ultrasonic standing waves.6-8 Particles, blood cells, bacteria, even colloids may be efficiently manipulated with ultrasound9,10 with frequencies in the range of 0.5-10 MHz. Species tend to focus either at the nodes or at the antinodes of the standing wave depending on their positive or * To whom correspondence should be addressed. E-mail: hoyos@ pmmh.espci.fr. (1) Hawkes, J.; Coakley, W. Sens. Actuators, B 2001, 75, 213–222. (2) Petersson, F.; Nilsson, A.; Holm, C.; Jo ¨nsson, H.; Laurell, T. Lab Chip 2005, 5, 20–22. (3) Bazou, D.; Dowthwaite, P.; Khan, I.; Archer, C.; Ralphs, J.; Coakley, T. Mol. Membr. Biol. 2006, 23, 195–205. (4) Coakley, W.; Hawkes, J.; Sobanski, M.; Cousins, C.; Spengler, J. Ultrasonics 2000, 38, 638–641. (5) Marmottant, P.; Hilgenfeldt, S. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 9523–9527. (6) King, L. Proc. R. Soc. London, Ser. A: Math. Phys. Sci. 1934, 147, 212– 240. (7) Yoshioka, K.; Kawashima, Y. Acoustica 1955, 5, 167–173. (8) Townsend, R.; Hill, M.; Harris, N.; White, N. Ultrasonics 2004, 42, 319– 324. (9) Johnson, D.; Feke, D. Sep. Technol. 1995, 5, 251–258. (10) Mandralis, Z.; Feke, D. AIChE J. 1993, 39, 197–206.

1318

Analytical Chemistry, Vol. 82, No. 4, February 15, 2010

negative acoustic impedance contrast. While acoustic resonators allow manipulation of particulate materials when combined with flow fields mostly in microfluidic devices, applications to segregation of species of different sizes and/or different acoustic impedance contrast in higher throughput separators are still not developed. Studies are mostly devoted to separation of suspended matter from liquids or to separation of species of opposite impedance, the latter illustrated by separation of red blood cells from lipids in whole blood in a microfluidic device.11 One way of generating preparative separations using standing wave fields is to combine an acoustic radiation force with an axial flow in a SPLITT fractionation channel. The split-flow lateraltransport thin channel fractionation (SPLITT) technique12 makes use of ribbonlike channels, or Hele-Shaw cells with a high aspect ratio, provided with two inlets and two outlets where the flows merge and separate in the channel thickness. An axial flow may be combined with transversal force fields like gravitational,13 magnetic,14,15 or electric16 in order to generate a differential lateral transport of suspended materials depending on their physicochemical properties. Using an acoustic force in SPLITT-like fractionation channels is not common. Some devices using microfluidic systems of several inlets and outlets with very low throughput have been set up for specific applications,17 but separation in size of particulate materials using an acoustic-SPLITT device has not been reported. In this article, we demonstrate the continuous separation of solid particles without using membranes or other filters by combining hydrodynamic flows and an acoustic force. The separation presented and the resolution reached in this work have never been performed in SPLITT fractionation. Compared to other existing acoustic devices, the originality of ours is the acoustic programming. This approach can be applied to both microfluidic and high-throughput separations. Even though we shall make reference only to separation of solid particles, this technique can be extended to cells, phospholipid vesicles, liposomes or bacteria. The proposed separation device will be generally referred to as a hydrodynamic acoustic sorter (HAS) and when applied to cell (11) Laurell, T.; Petersson, F.; Nilsson, A. Chem. Soc. Rev. 2007, 36, 492–506. (12) Giddings, J. Sep. Sci. Technol. 1985, 20, 749–768. (13) Benincasa, M.; Moore, L.; Williams, P.; Poptic, E.; Carpino, F.; Zborowski, M. Anal. Chem. 2005, 77, 5294–5301. (14) Jiang, Y.; Miller, M.; Hansen, M.; Myers, M.; Williams, P. J. Magn. Magn. Mater. 1999, 194, 53–61. (15) Zborowski, M.; Williams, P.; Sun, L.; Moore, L.; Chalmers, J. J. Liq. Chromatogr. Relat. Technol. 1997, 20, 2887–2905. (16) Narayanan, N.; Saldanha, A.; Gale, B. Lab Chip 2006, 6, 105–114. (17) Petersson, F.; Aberg, L.; Nilsson, A.; Laurell, T. Anal. Chem. 2007, 79, 5117–5123. 10.1021/ac902357b  2010 American Chemical Society Published on Web 01/25/2010

Figure 1. Schematic view of a s-SPLITT channel.18,19 The dashed lines represent the inlet splitting plane (ISP) and the outlet splitting plane (OSP). Thus, the distance wa′ represents the thickness of the injected layer through the upper input and wb the thickness of the layer extracted through the lower output.

separation as a hydrodynamic acoustic cell sorter, HACS. In the first section we present the HAS separation scheme, which is based on a space programmed acoustic field set up in a stepSPLITT channel, s-SPLITT, which is a channel where the flow splitters are replaced by steps.18-20 In the next section we present the theoretical aspects related to ultrasonic standing waves and we introduce the separation method. In the experimental section, we present the setup and parameters used for separation with a homemade HAS device, and the section is complemented by a theoretical modeling. Finally, we present the results and the discussion. THEORY AND MECHANISM Forces Acting on the Particles. During the acoustic separation process, particles in a SPLITT channel (see Figure 1) experience several forces and hydrodynamic interactions: the acoustic force, the drag force, the buoyancy force, and particleparticle and particle-wall interactions. However, as we work with dilute suspension, particle-particle interactions will be neglected here. In addition, as will be shown later, particles will remain far from the walls so we shall not take into consideration particle-wall interactions. For the sake of clarity, we will recall the expression of drag force, buoyancy,21 and acoustic force.7 Drag Force. The expression of the drag force is b b-b Fd ) 6πηr(U v)

(1)

where η is the dynamic viscosity of the fluid, r is the radius of b is the fluid velocity, and b particles, U v is the particle velocity. A Poiseuille flow is established in the channel, with a parabolic profile given by the following relationship, the origin of the x axis is at the lowest wall (see Figure 1): b ) 6U ¯x 1- x b U e w w x

(

)

(2)

(18) Hoyos, M.; Kurowski, P.; Callens, N. Patent No. FR 05 50645, 2006, 1, 130. (19) Callens, N.; Hoyos, M.; Kurowski, P. Anal. Chem. 2008, 80, 4866–4875. (20) Hoyos, M.; Nino, A.; Camargo, M.; Diaz, J.; Leon, S.; Camacho, M. J. Chromatogr., B 2009, 877, 3712–3718. (21) Landau, L.; Lifshitz, E. In Fluid Mechanics; Butterworth-Heinemann: Oxford, U.K., 2000; Chapter 1, p 1.

¯ is the average flow velocity and w the channel where U thickness. The horizontal velocity of each particle is driven only by the x component of that force and will therefore be always close to the fluid velocity. The y component of the drag force constitutes a friction force and is expressed as -6πηrv by. Buoyancy. The net force resulting from buoyancy and particle weight reads 4 3 ez b Fb ) 3 πr g(Ff - Fp)b

(3)

where g is the standard gravity and Ff and Fp are the fluid and the particle densities, respectively. Acoustic Force. The principal effect of the acoustic force is to drag injected species toward the nodes of the pressure field. These nodes move in the case of a progressive wave but remain fixed in the case of a standing wave. The pressure field in the latter case reads22 p(x, t) ) p0 cos(kx) cos(ωt)

(4)

where p0 is the pressure wave amplitude, k ) nπ/w is its wavenumber, with n an integer, ω ) 2πf is its pulsation, with f as the frequency. To use such a wave will allow us to focus species at specific places in the channel. Particles suspended in a fluid where such an acoustic standing wave is applied undergo the following acoustic force:6,23 4 b Fac ) A πr3εjk sin(2kx)b ex 3

(5)

where jε stands for the mean acoustic energy per unit of volume. It is worth noting that the energy density is an unknown parameter in experiments and needs to be determined independently, as will be explained in the experimental section. The dimensionless parameter A, called impedance contrast factor, has the following expression: (22) Landau, L.; Lifshitz, E. In Fluid Mechanics; Butterworth-Heinemann: Oxford, U.K., 2000; Chapter 8, p 251. (23) Hasegawa, T.; Yosioka, K. J. Acoust. Soc. Am. 1969, 46, 1139.

Analytical Chemistry, Vol. 82, No. 4, February 15, 2010

1319

Figure 3. Acoustic SPLITT fractionation principle (see text). Figure 2. (Left) Graph of the acoustic force and the corresponding pressure field for one- (n ) 1) and two-node (n ) 2) waves. The number of nodes follows the relationship: w ) n(λ/2) with λ as the wavelength. (Right) Acoustic potential from which the force derivates for the same values of n. Minima of potential, which are stable equilibrium positions, have the same position as the pressure nodes: particles are attracted toward these nodes.

A)

cf2Ff 3Fp + 2(Fp - Ff) - 2 2Fp + Ff cp Fp

(6)

where cp and cf are, respectively, the sound speed in particles and in the fluid. A can be either positive or negative depending on particle characteristics. We will restrict our discussion to positive A as it is the case for most of the particles we are interested in (vesicles, blood cells. . .).11 The acoustic force derivates from the following potential energy εj 4 V ) A πr3 cos(2kx) 3 2

(7)

This potential energy shows minima at each of the n pressure nodes. Hence particles are pushed toward these nodes as can be seen in Figure 2. The intensity of the acoustic force upon a particle depends on its volume and its impedance contrast factor. It is thus possible to generate selectivity based on those physicochemical parameters. We note that acoustic impedance contrast becomes here a new selectivity parameter in SPLITT-like separation methods. Separation with Acoustic Programming Force. The main effect of buoyancy when the acoustic force is applied, is to shift downward the equilibrium positions of particles. Both forces scale bb as r3, this implies that the equilibrium positions, given by b Fac+F b ) 0, do not depend on particle size. Thus the use of an acoustic standing wave does not allow realizing particle separation in size once the species have reached their equilibrium position. In contrast, the characteristic time, or relaxation time, taken by particles to reach their equilibrium positions depends on the particle size as it results from the competition between the acoustic and drag forces. It scales approximatively with ηδ/ (r2Aεjk), where δ is the distance between the node and the initial particle position. This relationship is obtained by comparing eq 5 with eq 1 and by considering the relaxation time as the product of an average transversal velocity and the particle initial distance to the node. Our separation scheme is based on this 1320

Analytical Chemistry, Vol. 82, No. 4, February 15, 2010

dependence of the relaxation time on the particle size: by properly choosing the residence time, the magnitude of the acoustic field, and frequencies, particles can be efficiently separated across the channel thickness. This is reminiscent of the so-called hyperlayer fractionation mode in field-flow fractionation (FFF)24 and SPLITT,25 where inertial lift forces26 are acting upon particles. Let us note that both techniques, FFF, which is analytical, and SPLITT, which is preparative, have exploited differences in relaxation times, and separations depend on differences in equilibrium position. The principle of the separation is depicted in Figure 3. We consider a mixture of two different species injected at the upper inlet of a SPLITT (or s-SPLITT) channel. Two transducers with different frequencies are placed closely along the channel and generate ultrasonic standing waves in the channel thickness. The first transducer, by generating a single-node wave, induces a primary separation through the difference in relaxation time of the different species. In the gap between the two transducers, particles are freely settling. Particles with the smaller relaxation time end up in the lower half of the channel while those having the bigger relaxation time will remain in the upper half. The second transducer, by generating a two-node wave, drives the separated species to the nodes while keeping them far from the walls. Particles in the lower half are guided toward the lower outlet, while particles in the upper half are guided toward the upper outlet. We will refer to this configuration of acoustic waves as the (1-2) configuration. Many other configurations are possible in our acoustic programming technique, in function of separations required. Note that the separation is induced by the difference in the relaxation time of the different species, which is controlled by the injection position and the first wave amplitude. In fact, sedimentation alone, under particular conditions, could generate selectivity, like in conventional SPLITT fractionation, but by using the proposed programmed acoustic field, we have one more control parameter, the wave amplitude, i.e, the acoustic force, in some extent analogous to a variable centrifugal force. Moreover, the selective transverse migration is faster than that generated by gravity alone as will be shown later. In the technique presented here, the throughput will be highly improved with respect to conventional gravitational SPLITT as we shall see later on. (24) Ratanathanawongs, K.; Giddings, J. Anal. Chem. 1992, 61, 6–15. (25) Zhang, J.; Williams, P.; Myers, M.; Giddings, J. Sep. Sci. Technol. 1994, 29, 2493–2522. (26) Ho, B.; Leal, G. J. Fluid Mech. 1976, 76, 783–799.

EXPERIMENTAL SECTION AND MODELING Experimental Device. The device is composed of a homemade step-SPITT channel comprising two inlets and two outlets. The channel of 70 mm × 7 mm × 0.4 mm ) 196 mm3 has been built by using one plate in plastic material and the other in glass; in between, Mylar spacers have been inserted. The inlet and outlet part of the s-SPLITT channel are similar to the classic SPLITT device but with the splitters replaced by steps.18 Ultrasonic transducers in ceramic P52, Noliac ceramics, Czech Republic, of surface 5 mm × 10 mm ) 50 µm2 of 2 and 4 MHz nominal resonance frequency have been used; the channel resonance for optimal standing wave were 1.68 and 3.3 MHz. The process of determining the channel resonance is not trivial and will be the subject of a forthcoming paper. We verified the resonance by in situ observation of the particle focusing by microscopy. Transducers were placed as pairs of emitters and receivers on opposite walls; this configuration optimizes the reflection of ultrasonic waves at 20 and 40 mm away from the inlet step. The potential difference applied to transducers was 20 V peak to peak. Here we need to stress on the fact that this potential is related to the wave amplitude which has to be converted in the average acoustic energy density jε. There is not a simple way of doing that because energy is absorbed and dissipated by the different layers between the transducer and the resonant cavity; energy is also dissipated by cables and by the mechanic coupling between the transducers and the walls. The applied voltage used was the maximum accepted by our transducers and corresponding to the better results. Transducers were fixed by means of a pressure device and the acoustic coupling was accomplished by ultrasound gel. The diluted sample was composed of a mixture of 5 and 10 µm Coulter Standard latex particles, Beckman Coulter, suspended in deionized water; the volume fraction was around 0.1%. Flow injection was performed by using syringe pumps by KDS Scientific. The experimental procedure was as follows: the particle mixture was injected at the inlet a′ at a flow rate Qa′ ) 6 mL/h; the carrier, deionized water, was injected at the inlet b′ at Qb′ ) 12 mL/h for a total flow rate Q ) Qa′ + Qb′ ) 18 mL/h. The corresponding average axial velocity was 2 mm/ s. The position of the ISP (see Figure 1), labeled as wa′ ) 0.39w ) 156 m, was calculated by using the classical expression Qa′/Q ) 3(wa′/w)2 - 2(wa′/w)3 ) 0.33, where w is the channel thickness. The separation was carried out as schematized in Figure 3. In situ observation of the concentration profiles was realized 3.5 mm after the second pair of transducers. In Situ Observation by Digital Holgraphic Microscopy. In order to in situ observe the separation generated by the acoustic programming field, we used a digital holographic microscope, DHM, with partially coherent illumination; details about the DMH can be found in refs 27 and 28 and references cited therein. The holographic microscope is composed of a Mach-Zehnder interferometer29 using a 626 nm wavelength laser beam. This microscope allows observing the 3D time evolution configuration of (27) Dubois, F.; Novella, M.; Minetti, C.; Monnom, O.; Istasse, E. Appl. Opt. 2004, 43, 783–799. (28) Dubois, F.; Callens, N.; Hoyos, M.; Kurowski, P.; Yourassowski, C.; Monnom, O. Appl. Opt. 2006, 45, 3893–3901. (29) Born, M.; Wolf, E. In Principles of Optics; Pergamon Press: Oxford, U.K., 1975; Chapter7, p 256.

particles in a window of 300 × 400 mm2. The holograms composed of diffraction patterns are recorded in a CCD camera operating at 24 images per seconds during 25 s, for a total of 600 images for each experiment. The holographic reconstruction of each image has been undertaken by solving the 2D Kirchhoff-Fresnel diffraction equation. Details about the procedure can be found in refs 27 and 28 and references cited therein. Particle Trajectory Calculations. In order to compare experiments with a hydrodynamic modeling, we computed the particle trajectories during their migration through the channel under the influence of acoustic and gravity forces; we numerically integrated Newton’s law with the fourth-order Runge-Kutta method.30 Newton’s law applied to a particle in the channel reads as 1 b dv b ) (F +b Fb + b Fd) dt m ac

(8)

The Runge-Kutta method is an iterative procedure which allows one to integrate a first order ordinary differential equation: du b ) f(u b, t) dt

(9)

where f is a known function of b u and t. We thus reformulate Newton’s law in the following manner:

[] [

b v x d b ) b (Fac + b Fb + b Fd)/m v dt b

]

(10)

As accelerations of particles could be high, it is necessary to use a short time step, of the order of 10 µs. However, once particles have converged, their accelerations are much smaller. So we have implemented a method with an adaptive time step30 to speed up the calculations. In addition, we have made the following assumptions: (a) the acoustic waves are perfect stationary waves so that we can use eq 5 of the acoustic force; (b) the divergence of the acoustic fields is not taken into account, so that the waves have a square-shaped transverse profile; and (c) the flow has a parabolic profile all along the channel. RESULTS AND DISCUSSION Experiments for separating latex particles of 5 and 10 µm have been conducted, and in situ observations have been made by DHM. 3D observations allowed us to make a cumulated concentration profile in the channel thickness. Binary Separation of Latex Particles. The example in Figure 4a is the superposition of 10 holograms recorded at equally spaced times during one run. We observe out of focus particles with diffraction rings, the microscope was focused at the midchannel thickness. Figure 4b is the reconstructed image of the plane corresponding to the position of the lower pressure node of the dual wave. Concentration profiles are obtained by counting all the focused particles at each level of reconstruction, namely, every 1 (30) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. In Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed.; Cambridge University Press: Cambridge, U.K., 1992; Chapter 16, pp 704716.

Analytical Chemistry, Vol. 82, No. 4, February 15, 2010

1321

Figure 4. Holographic reconstruction of two planes in the channel thickness: (a) the middle of the channel plane and (b) the lower node position of the second wave. We can see that 10 µm particles belong to the latter.

5a shows particle distributions of both sizes without an acoustic field, i.e., when particles settle under gravity, equivalent to conventional gravitational SPLITT, observed by the DHM. We can see that a partial separation in a zone of the channel thickness spreading out about 180 µm. Particles had time to settle only a little more than half of the channel thickness. Figure 5b represents the distribution of particles when only the 4 MHz transducer, dual node wave, is on, which means that the presorting generated by the first 2 MHz transducer is still not operating. Complete separation is observed, but all the particles are focused close to the upper node because, as shown the result without acoustics, particles did not have time to settle further than the midchannel thickness. Let us note that particles spread out in a zone narrower than the former situation, about 50 µm, and species are are very close. Finally, Figure 5c shows the distribution of the mixture when the first acoustic field is also applied. We clearly see the improvement leading to a complete separation of both species. They are focused at the nodes, thereby separated by 200 µm. We also observe the narrow distributions in the thickness resulting from the efficient action of the acoustic force, reducing the effects like the shear induced diffusion mentioned in the introductory material. A thorough experimental study is underway and will be the subject of a forthcoming paper.

Figure 5. Normalized cumulated number profile of latex beads determined by holographic microscopy. Here the origin of the x axis is taken at the focal point of the microscope, at the middle of the channel thickness: (a) acoustic off, (b) dual nodes wave on, and (c) single and dual node waves on.

µm. The concentration profiles obtained represent more than 1000 holographic reconstructions. Distributions presented in Figure 5 are the normalized cumulated counts of particles in the whole channel thickness, the origin of the x axes are situated at the midchannel thickness, about 200 µm, with the bottom wall being situated at x ) -200 µm. Figure 1322

Analytical Chemistry, Vol. 82, No. 4, February 15, 2010

RESULTS OF THE MODELING Binary Separations. In order to compare the experimental results with theory, we inserted the experimental parameters in the calculations of particle trajectories. Figure 6 shows trajectories of latex particles (Fp ) 1.05 g/cm3 and cp ) 2407 m/s) of 5 and 10 µm diameter, suspended in water with Ff ) 1 g/cm3 and cf ) 1480 m/s, flowing through a 400 µm thick and 3 cm length channel. A first wave with one pressure node acts on the first 10 mm, and a second wave with two pressure nodes acts on the last 10 mm of the channel. Between these two zones where acoustic and gravitational forces are superimposed, particles experience only the gravitational field along 10 mm. The average flow velocity is 2 mm/s. In this (1-2) configuration, the relaxation time of 5 µm particles injected between 300 and 400 µm above the lower wall is longer than their residence time into the first acoustic field; therefore, they remain in the upper half of the channel thickness. On the contrary, 10 µm particles almost reach their equilibrium position at the lower

Figure 7. Cutoff diameter at the two node zone as a function of the average flow velocity and the acoustic energy density for latex particles injected 350 µm above the lower wall. Figure 6. Particle trajectories computed for acoustic separation using two transducers in series. The first transducer (one pressure node) is placed on the first 10 mm and the second one (two pressure nodes) at the last of the channel length; in between, particles are settling under gravity. Particles are injected in a 100 µm layer thickness.

half of the channel. Both species are then focused on different nodes by the second wave and end up separated by 200 µm. We observe that the theoretical modeling is in agreement with the experimental results. In fact, the model predicts that all particles should be focused at the two nodes, without any significant broadening in the distribution. It is apparent that that situation did not happen in real experiments. Besides that fact, other nonidealities have to be considered for explaining the broad distributions observed in the real experiment. First in a real channel it will not be possible to set up a perfect standing wave. This is due to the several interfaces that will be present on the path of the wave through the channel. It will result in a displacement of the nodes and in a reduction of acoustic force intensity. However the general features of the acoustic force will remain the same (particles will be driven to the nodes with a relaxation time having the same dependence on their size), and thus the separation principle does not change. Second, the transverse profile of the waves is not square-shaped. This will also result in a change of the relaxation times, as the amplitude of the force will vary across the width of the acoustic wave. However, with the transducer geometry used, the divergence of the beam is only a few degrees and this effect can be neglected. Influence of Parameters. To quantitatively study the influence of parameters involved in the separation, we introduce the cutoff diameter dc such that particles smaller than this diameter are driven toward the upper node, while larger ones are driven toward the lower node. As noted earlier, for given particle composition and channel geometry, the cutoff diameter depends on three parameters: the initial position of the particle relative to the node, the flow rate, and the wave amplitude. Indeed one must compare the residence time in the first acoustic field, given by the flow rate, and the relaxation time, scaled as δ/(r2jε). In Figure 7 is depicted the dependence of the cutoff diameter, represented by curves of equal cutoff, on the acoustic energy density (i.e., the wave amplitude), and the average flow velocity (i.e the flow rate), for latex particles injected 350 µm above the lower wall. We assume that the energy density is the same for ¯ ) corresponds a diameter both transducers. To each couple (εj, U above which particles will be directed to the lower node. On the

Figure 8. Proportion of particles collected at the two nodes zone on the upper node as a function of the particle diameter for two different initial layers thickness 100 and 10 µm, centered at 350 of the channel thickness.

one hand, for a given flow velocity, increasing the acoustic energy density reduces the cutoff diameter. This is because the relaxation time of particles is reduced leading to a sufficient reduction in the size of particles to approach the equilibrium position during the primary relaxation. On the other hand, the flow rate determines the residence time of the particles in the first acoustic field. As the flow rate is increased, the maximum relaxation time for which particles are dragged to the lower part of the channel is reduced, hence the cutoff radius increases. Such a graph shows the possibility to choosing the separation parameters by setting up the appropriate flow rate and acoustic energy density for optimizing separation. Concerning the energy density, we can conclude that in our experiments it should be higher than 2 J/m3 for performing the entire binary separation. Let us note that values around 3 J/m3 have been determined and used by other authors who achieved acoustic focusing of latex particles.1 A new way for determining the acoustic energy density will be presented in a forthcoming paper. Injecting particles higher in the channel thickness also increases the cutoff diameter, as it increases the distance to be covered by the particles to reach the lower part of the channel. It is thus important to use a thin layer to have a well-defined cutoff, as can be seen in Figure 8. However, for a classical SPLITT channel, it is not possible to choose the initial position of the particles independently of the layer thickness wa′, thus only this latter parameter can be controlled in conventional SPLITT fractionation. The initial position of the particles is no longer a Analytical Chemistry, Vol. 82, No. 4, February 15, 2010

1323

separation parameter in practice. In contrast, when using a three-input s-SPLITT channel (three inlets and two steps) one can independently choose the layer position and thickness by performing inlet hydrodynamic focusing of particles, which makes use of such a channel very interesting in this context. Finally, we can make multidimensional figures including acoustic impedance, density, injection particle position, and so on, but this thorough analysis is beyond the objectives of this study and will be included in the next experimental paper. Comparison with Other SPLITT Fractionation. The acoustic force intensity is not constant across the channel thickness, thus particle trajectories depend on more operating parameters than gravitational, magnetic, or electrical SPLITT as well as SPLITT with inertial lift forces. A general model predicting the concentration profile at the outlet needs to consider particle initial positions, acoustic field forces, and flow characteristics. A common parameter in SPLITT fractionation, required for studying selectivity and resolution, is the cutoff diameter,31 dc:

dc )



18η(Qa - Qa') Lbg∆F

(11)

where Qa and Qa′ are, respectively, the outlet flow rate in a and the inlet flow rate in a′, b and L are the channel breadth and length. For any physicochemical parameter, when a constant field force F is acting upon particles all along the channel, it is possible to determine the OSP position required to drive species whose mobility M ) v/F, with v the transversal migration velocity, is higher than a certain value, cutoff mobility, toward the outlet b opposite to the injection inlet a. The cutoff mobility in SPLITT fractionation has been well studied in gravitational31 and magnetic SPLITT fractionation.15 The cutoff mobility in the inertial lift forces mode of operation can be also determined even though the force is not constant in the channel thickness by using classical models already established.25,32 A high number of parameters are involved in HAS, and cutoff mobility is more complicated to establish. In this article, we start our reflection about the relevant parameters leading to optimize separations and to predict selectivity and resolution in hydrodynamic-acoustic fractionation. The latter concepts will not be defined in this preliminary experimental study. In order to show the HAS improvements with respect to the gravitational SPLITT fractionation, we computed the most favorable trajectories of the same latex particle mixture separated in a conventional SPLITT channel. Figure 9 shows trajectories computed by the ideal model currently used in SPLITT. The parameters are the same used before, but in order to obtain the best separation, the flow rate has been modified with respect to that used in s-SPLITT with programmed acoustic field. The result shows that the optimum flow rate is 2 mL/h to be compared to 18 mL/h in acoustic separation. We may conclude that the throughput should be much higher, about 1 order of magnitude in this particular case, using the HAS. Nevertheless, the throughput can still be improved by increasing both the flow rate and the acoustic energy density. This is a major finding of the acoustic (31) Giddings, J. Sep. Sci. Technol. 1992, 27, 1489–1504. (32) Williams, P. Sep. Sci. Technol. 1994, 29, 11–45.

1324

Figure 9. Separation by gravitational SPLITT fractionation.

Analytical Chemistry, Vol. 82, No. 4, February 15, 2010

Figure 10. Acoustic sorting using two online transducers for ternary separation. The channel length is 5 mm, the acoustic energy per unit of volume is 3 J/m3 for both waves, and the average velocity is 5 mm/s.

programming technique that not only shows a much better peak separation but the throughput is highly improved by 1 order of magnitude. Ternary Separations. In order to demonstrate the versatility of the acoustic programming s-SPLITT fractionation, we computed trajectories leading to separations of more than two species, simply by adjusting the number of nodes. Figure 10 shows an example of ternary separation by depicting the trajectories of silica particles of Fsi ) 2.5 g/cm3, csi ) 3000 m/s, and diameter 2, 4, and 6 µm in a 500 µm channel thickness. In the (1-3) configuration, the second transducer generates a three-node stationary wave. In such a configuration, one can define two cutoff radii to describe the separation. We shall not get into further details about the (1-3) configuration in the present work. Compared to conventional SPLITT fractionation, the HAS configuration highly increases the throughput which is the most important parameter to optimize in any preparative separation. This is the most important improvement of the HAS device. In this work we succeed in the complete binary separation of 5 and 10 µm particles, separation never reported in any other work in SPLITT fractionation. In fact, all binary separations reported have been performed using polydisperse samples, the polydispersity being progressively reduced by reinjecting the sample in the channel. We note that the high-resolution separation of micrometersized particles are currently achieved in FFF, but FFF and SPLITT cannot be compared as they are very different even though they

belong to the same family of separation techniques. While FFF is an analytical technique and the separation occurs along the channel, SPLITT fractionation is a preparative technique and the separation is operated in the channel thickness. The operational parameters are different, and the performance follow different criteria.33 This new scheme of separation is very promising because of its excellent theoretical efficiency (which is limited only by the minimal achievable thickness of the initial layer of particles) and its great versatility. Indeed, just one experimental device is required to achieve the different separations, because of the high number of control parameters that can be manipulated. Changing the nature of species to separate (that is to say changing A and/ or size) requires just adjustment of the values of jε and of the flow rate to obtain the desired cutoff diameter. Moreover, using a SPLITT (or s-SPLITT) channel allows one to perform separations (33) Giddings, J. C. In Unified Separation Science; John Wiley & Sons: New York, 1991; Chapter 9, p 189.

with high throughput, which is very promising for industrial applications. Finally, it is worth noting that a similar scheme can be applied to particles having the same size but different, not only opposite, impedance contrast factor, as the relaxation time depends on A. In conclusion, the HAS, which combines a s-SPLITT fractionation channel with a programmed acoustic force, represents a major improvement of the SPLITT fractionation technique, and its versatility allows one to foresee a great number of new biotechnological applications. ACKNOWLEDGMENT This work was supported by CNRS and by CNES Aide L´ la Recherche project. We are grateful to Michel Martin and Steve Williams for very fruitful discussions. Received for review October 17, 2009. Accepted January 5, 2010. AC902357B

Analytical Chemistry, Vol. 82, No. 4, February 15, 2010

1325